The present invention relates generally to methods and apparatuses for test pattern selection for computational lithography model calibration. According to some aspects, the pattern selection algorithms of the present invention can be applied to any existing pool of candidate test patterns. According to some aspects, the present invention automatically selects those test patterns that are most effective in determining the optimal model parameter values from an existing pool of candidate test patterns, as opposed to designing optimal patterns. According to additional aspects, the selected set of test patterns according to the invention is able to excite all the known physics and chemistry in the model formulation, making sure that the wafer data for the test patterns can drive the model calibration to the optimal parameter values that realize the upper bound of prediction accuracy imposed by the model formulation.
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1. A computer-implemented method of test pattern selection for computational lithography model calibration, the method comprising: preparing a sensitivity matrix having matrix elements corresponding to, and thereby defining a sensitivity relationship between, a pool of candidate test patterns and a set of model parameters, wherein the matrix elements quantify how changes in measurements from imaging the test patterns using a lithographic process corresponding to the set of model parameters are induced by changes in the set of model parameters; performing calculations using the sensitivity matrix; and selecting, by the computer, a set of test patterns from the pool of candidate test patterns based on the calculations using the sensitivity matrix.
This is a computer-based method for selecting the best test patterns to calibrate computational lithography models. First, it creates a "sensitivity matrix" linking candidate test patterns to model parameters. This matrix quantifies how changes in measurements from imaged test patterns (using the lithographic process) are affected by changes in the model parameters. Then, the computer performs calculations on this matrix and selects a set of test patterns from the candidate pool, based on these calculations, for calibrating the lithography model.
2. A method according to claim 1 , wherein the selecting step includes: identifying which test pattern of the pool of candidate test patterns has the greatest sensitivity to certain of the set of model parameters; and adding the identified candidate test pattern to the set of test patterns.
Building upon the method of selecting test patterns for lithography model calibration by using a sensitivity matrix, the test pattern selection involves identifying the candidate test pattern that is most sensitive to specific model parameters. This most sensitive test pattern is then added to the selected set of test patterns to be used for calibration.
3. A method according to claim 2 , further comprising repeating the performing, identifying and adding steps until test patterns corresponding to all of the set of model parameters have been added to the selected set of test patterns.
Expanding on the method of selecting test patterns for lithography model calibration, after a test pattern with the greatest sensitivity is identified and added to the selected set, the process of performing calculations on the sensitivity matrix, identifying the most sensitive test pattern, and adding it to the selected set is repeated. This repetition continues until test patterns representing all model parameters have been added to the selected set. This ensures comprehensive coverage of all relevant parameters in the lithography model.
4. A method according to claim 1 , wherein the step of performing calculations includes performing principal component analysis on the sensitivity matrix.
In the method of selecting test patterns for lithography model calibration using a sensitivity matrix, the calculations performed on the sensitivity matrix include Principal Component Analysis (PCA). PCA helps identify the most significant relationships between test patterns and model parameters, improving the efficiency and accuracy of test pattern selection.
5. A method according to claim 1 , wherein the step of preparing the sensitivity matrix includes estimating wafer measurement uncertainties based on a simulated aerial image corresponding to the pool of candidate test patterns.
In the method of selecting test patterns for lithography model calibration by using a sensitivity matrix, preparing the sensitivity matrix includes estimating wafer measurement uncertainties. These estimations are based on simulated aerial images of the candidate test patterns. This allows for incorporating potential measurement errors into the selection process, leading to more robust calibration.
6. A method according to claim 1 , wherein the step of preparing the sensitivity matrix includes simulating an aerial image based on a mask including the pool of candidate test patterns and using nominal values of certain of the set of model parameters.
In the method of selecting test patterns for lithography model calibration using a sensitivity matrix, the sensitivity matrix is prepared by simulating an aerial image. This simulation uses a mask containing the candidate test patterns and uses default (nominal) values for the model parameters. This simulation provides the data needed to establish the relationship between test patterns and model parameter sensitivity.
7. A method according to claim 1 , wherein the selecting step includes minimizing a cost function related to model accuracy.
In the method of selecting test patterns for lithography model calibration using a sensitivity matrix, the selection of test patterns involves minimizing a "cost function." This cost function represents the desired accuracy of the lithography model. The test patterns are chosen to minimize this function, leading to the most accurate model calibration.
8. A method according to claim 7 , wherein the cost function represents CD prediction errors for a certain pool of patterns, including a full chip pattern set.
Building upon the method of selecting test patterns for lithography model calibration by minimizing a cost function, the cost function represents critical dimension (CD) prediction errors for a set of patterns. This pattern set can include a full chip pattern set, ensuring that the selected test patterns are optimized for predicting CD variations across the entire chip design.
9. A method according to claim 1 , wherein preparing the sensitivity matrix includes calculating G×P distinct matrix elements, where G is the number of test patterns in the pool of candidate test patterns, and P is the number of the set of model parameters.
In the method of selecting test patterns for lithography model calibration using a sensitivity matrix, developing the sensitivity matrix involves calculating a number of matrix elements equal to G multiplied by P. Here, G is the number of candidate test patterns, and P is the number of model parameters. This calculation quantifies the sensitivity relationship between each test pattern and each model parameter.
10. A method according to claim 1 , wherein preparing the sensitivity matrix includes calculating changes in measurements associated with the pool of candidate test patterns as a function of changes in the set of model parameters.
In the method of selecting test patterns for lithography model calibration using a sensitivity matrix, preparing the sensitivity matrix includes calculating how measurements associated with the test patterns change based on changes in the model parameters. This calculation establishes a direct link between the test patterns and the parameters they help to calibrate.
11. A computer-implemented method of test pattern selection for computational lithography model calibration, the method comprising: developing a sensitivity matrix that corresponds to a cost function associated with accuracy of a lithography model, wherein the sensitivity matrix establishes a relationship between a pool of candidate test patterns and a set of parameters of the lithography model, and wherein the sensitivity matrix comprises matrix elements that quantify how changes in measurements from imaging the test patterns using a lithographic process corresponding to the lithography model are induced by changes in the set of parameters of the lithography model; and selecting, by the computer, a set of test patterns from the pool of candidate test patterns by performing calculations on the sensitivity matrix.
This is a computer-based method for selecting the best test patterns to calibrate a lithography model. It involves creating a "sensitivity matrix" linked to a cost function representing the desired model accuracy. This matrix quantifies how changes in measurements from imaged test patterns (using the lithographic process) are affected by changes in the model parameters. Then, the computer performs calculations on this matrix and selects a set of test patterns from the candidate pool, based on these calculations, for calibrating the lithography model.
12. A method according to claim 11 , wherein the selecting step includes: determining which one of the candidate test patterns has a greatest sensitivity to an identified model parameter using results of the calculations; and adding the determined test pattern to the selected set of test patterns.
Expanding on the method of selecting test patterns for lithography model calibration using a sensitivity matrix tied to a cost function, the test pattern selection involves identifying the candidate test pattern that is most sensitive to an identified model parameter using the calculations performed on the sensitivity matrix. This most sensitive test pattern is then added to the selected set of test patterns to be used for calibration.
13. A method according to claim 12 , further comprising repeating the performing, determining and adding steps until test patterns corresponding to all of the set of model parameters have been added to the set of test patterns.
Building upon the method of selecting test patterns for lithography model calibration by using a sensitivity matrix tied to a cost function, after a test pattern with the greatest sensitivity is identified and added to the selected set, the process of performing calculations on the sensitivity matrix, determining the most sensitive test pattern, and adding it to the selected set is repeated. This repetition continues until test patterns representing all model parameters have been added to the selected set, thus ensuring comprehensive coverage of all relevant parameters in the lithography model.
14. A method according to claim 11 , wherein the step of performing calculations includes performing principal component analysis on the sensitivity matrix.
In the method of selecting test patterns for lithography model calibration using a sensitivity matrix tied to a cost function, the calculations performed on the sensitivity matrix include Principal Component Analysis (PCA). PCA helps identify the most significant relationships between test patterns and model parameters, improving the efficiency and accuracy of test pattern selection.
15. A method according to claim 11 , wherein the selecting step is performed so as to minimize a cost function.
In the method of selecting test patterns for lithography model calibration by using a sensitivity matrix tied to a cost function, the selection of test patterns is performed to minimize a cost function. This means test patterns are chosen that result in the lowest possible value for the cost function, indicating the best possible lithography model accuracy.
16. A method according to claim 15 , wherein the cost function represents CD prediction errors for a certain pool of patterns, including a full chip pattern set.
Building upon the method of selecting test patterns for lithography model calibration by minimizing a cost function, the cost function represents critical dimension (CD) prediction errors for a set of patterns. This pattern set can include a full chip pattern set, ensuring that the selected test patterns are optimized for predicting CD variations across the entire chip design.
17. A method according to claim 11 , wherein the step of developing the sensitivity matrix includes estimating wafer measurement uncertainties based on a simulated aerial image corresponding to the pool of candidate test patterns.
In the method of selecting test patterns for lithography model calibration using a sensitivity matrix tied to a cost function, developing the sensitivity matrix includes estimating wafer measurement uncertainties. These estimations are based on simulated aerial images of the candidate test patterns. This allows for incorporating potential measurement errors into the selection process, leading to more robust calibration.
18. A method according to claim 11 , wherein the step of developing the sensitivity matrix includes simulating an aerial image based on a mask including the pool of candidate test patterns and using nominal values of certain of the set of model parameters.
In the method of selecting test patterns for lithography model calibration using a sensitivity matrix tied to a cost function, developing the sensitivity matrix includes simulating an aerial image. This simulation uses a mask containing the candidate test patterns and uses default (nominal) values for the model parameters. This simulation provides the data needed to establish the relationship between test patterns and model parameter sensitivity.
19. A method according to claim 11 , wherein developing the sensitivity matrix includes calculating G×P distinct matrix elements, where G is the number of test patterns in the pool of candidate test patterns, and P is the number of the set of model parameters.
In the method of selecting test patterns for lithography model calibration using a sensitivity matrix tied to a cost function, developing the sensitivity matrix involves calculating a number of matrix elements equal to G multiplied by P. Here, G is the number of candidate test patterns, and P is the number of model parameters. This calculation quantifies the sensitivity relationship between each test pattern and each model parameter.
20. A method according to claim 11 , wherein developing the sensitivity matrix includes calculating changes in measurements associated with the pool of candidate test patterns as a function of changes in the set of model parameters.
In the method of selecting test patterns for lithography model calibration using a sensitivity matrix tied to a cost function, developing the sensitivity matrix includes calculating how measurements associated with the test patterns change based on changes in the model parameters. This calculation establishes a direct link between the test patterns and the parameters they help to calibrate.
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April 7, 2014
June 6, 2017
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